a: \(=\dfrac{4x-8+2x+4-8}{\left(x-2\right)\left(x+2\right)}=\dfrac{6x-12}{\left(x-2\right)\left(x+2\right)}=\dfrac{6}{x+2}\)

b: \(=\dfrac{-x+7x-4}{3x-2}=\dfrac{6x-4}{3x-2}=2\)

c: \(=\dfrac{x}{2x+1}-\dfrac{1}{\left(2x+1\right)\left(2x-1\right)}-\dfrac{\left(x-2\right)}{2x-1}\)

\(=\dfrac{2x^2-x-1-\left(x-2\right)\left(2x+1\right)}{\left(2x+1\right)\left(2x-1\right)}\)

\(=\dfrac{2x^2-x-1-2x^2-x+4x+2}{\left(2x+1\right)\left(2x-1\right)}\)

\(=\dfrac{2x+1}{\left(2x+1\right)\left(2x-1\right)}=\dfrac{1}{2x-1}\)

d: \(=\dfrac{5}{2x-3}+\dfrac{2}{2x+3}+\dfrac{2x-33}{4x^2-99}\)

\(=\dfrac{10x+15+4x-6+2x-33}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{16x-24}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{8}{2x+3}\)

a, (x-1).(x-2).(x-3)

= (x² - 2x - x + 2) . (x-3)

= (x² - 3x + 2). (x-3)4

= x³ - 3x² - 3x² + 9x + 2x -6

= x³ - 6x² + 11x -6

b) (x² +x+1)(x²-1)(x²-x+1)

= (x⁴ - x² + x³ - x+ x² -1) . (x² - x +1)

= (x⁴ + x³ -x -1) . (x² - x  +1)

= x⁶ - x⁵ + x⁴ + x⁵ - x⁴ + x³ - x² + x -1

= x⁶ + x³ - x² + x - 1

c) (2x-5)(4-3x)-(3x+11)(5-2x)-15(2x-5)

= (8x - 6x² - 20 + 15x) - (15x-6x+55-22x) - 30x + 75

= 8x - 6x² - 20 + 15x - 15x+6x-55+22x - 30x+75

= 6x-6x² +55

d)(x²-2x+3)(3x-5)-(x²+x-1)(2x+7)

làm tương tự phần C

lưu ý trước dấu ngoặc là dấu trừ, khi phá ngoặc ra phải đổi dấu



 

1)(x+1)(x+2)(x+3)=x³+6x²+11x+6

2)a)3x(x-5)-(x-1)(2+3x)=30

<=>3x²-15x-3x²+x+2=30

<=>-14x+2=30

<=>-14x=30-2

<=>-14x=28

<=>x=-2

b)(x+2)(x+3)-(x-2)(x+5)=0

<=>x²+5x+6-x²-3x+10=0

<=>2x+16=0

<=>2x=-16

<=>x=-8

c)(3x+2)(2x+9)-(x+2)(6x+1)=9

<=>6x²+31x+18-6x²-13x-2=9

<=>18x+16=9

<=>18x=9-16

<=>18x=-7

<=>x=-7/18

1: \(x\left(1-x\right)+\left(x-1\right)^2\)

\(=x-x^2+x^2-2x+1\)

=-x+1

3: \(\left(x+2\right)^2-\left(x-3\right)\left(x+1\right)\)

\(=x^2+4x+4-\left(x^2+x-3x-3\right)\)

\(=x^2+4x+4-\left(x^2-2x-3\right)\)

\(=x^2+4x+4-x^2+2x+3=6x+7\)

5: \(\left(x-2\right)^2+\left(x-1\right)\left(x+5\right)\)

\(=x^2-4x+4+x^2+5x-x-5\)

\(=2x^2-1\)

7: \(\left(1-2x\right)\left(5-3x\right)+\left(4-x\right)^2\)

\(=\left(2x-1\right)\left(3x-5\right)+\left(x-4\right)^2\)

\(=6x^2-10x-3x+5+x^2-8x+16\)

\(=7x^2-21x+21\)

9: \(\left(x+1\right)^2+\left(x-2\right)\left(x+2\right)-4x\)

\(=x^2+2x+1+x^2-4-4x\)

\(=2x^2-2x-3\)

11: \(\left(x+4\right)^2+\left(x+5\right)\left(x-5\right)-2x\left(x+1\right)\)

\(=x_{}^2+8x+16+x^2-25-2x^2-2x\)

=6x-9

13: \(\left(x-1\right)^2-2\left(x+3\right)\left(x-3\right)+4x\left(x-4\right)\)

\(=x^2-2x+1-2\left(x^2-9\right)+4x^2-16x\)

\(=5x^2-18x+1-2x^2+18=3x^2-18x+19\)

2: \(\left(x-3\right)^2-x^2+10x-7\)

\(=x^2-6x+9-x^2+10x-7\)

=4x+2

4: \(\left(x+4\right)\left(x-2\right)-\left(x-3\right)^2\)

\(=x^2-2x+4x-8-\left(x^2-6x+9\right)\)

\(=x^2+2x-8-x^2+6x-9=8x-17\)

6: (x-3)(x+3)-x(x+23)

\(=x^2-9-x^2-23x\)

=-23x-9

8: (x-2)(x+2)-(x-3)(x+1)

\(=x^2-4-\left(x^2+x-3x-3\right)\)

\(=x^2-4-\left(x^2-2x-3\right)\)

\(=x^2-4-x^2+2x+3=2x-1\)

10: \(\left(x+2\right)^2-\left(x+3\right)\left(x-3\right)+10\)

\(=x^2+4x+4-\left(x^2-9\right)+10\)

\(=x^2+4x+14-x^2+9=4x+23\)

12: \(\left(x-1\right)^2-\left(x-4\right)\left(x+4\right)+\left(x+3\right)^2\)

\(=x^2-2x+1-\left(x^2-16\right)+x^2+6x+9\)

\(=2x^2+4x+10-x^2+16=x^2+4x+26\)

a) \(\left(x^2-1\right)\left(x^2+2x\right)=x^4+2x^3-x^2-2x\)

b)  \(\left(2x-1\right)\left(3x+2\right)\left(3-x\right)=6x^2-3x+4x-2\left(3-x\right)\)

                                                          \(=6x^2-3x+4x-6+2x\)

                                                            \(=6x^2+3x-6\)

c) \(\left(x+3\right)\left(x^2+3x-5\right)=x^3+3x^2+3x^2+9x-5x-15\)

                                                  \(=x^3+6x^2+4x-15\)

d) \(\left(x+1\right)\left(x^2-x+1\right)=x^3+x^2-x^2-x+x+1\)

                                                \(=x^3+1\)

e) \(\left(2x^3-3x-1\right)\left(5x+2\right)=10x^4-15x^2-5x+4x^3-6x-2\)

                                                       \(=10x^4+4x^3-15x^2-11x-2\)

f) \(\left(x^2-2x+3\right)\left(x-4\right)=x^3-2x^2+3x-4x^2+8x-12\)

                                                 \(=x^3-6x^2+11x-12\)

a: \(=x^2+2x-8-x^2-2x-1=-9\)

b: \(=\dfrac{x^2+6x+9+3x-9+2x^2-18x}{x\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{3x^2-9x}{x\left(x-3\right)\left(x+3\right)}=\dfrac{3x\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}=\dfrac{3}{x+3}\)

\(a,\left(3x+x\right)\left(x^2-9\right)-\left(x-3\right)\left(x^2+3x+9\right)\)

\(=4x\left(x^2-9\right)-x^3+27\)

\(=4x^3-36x-x^3+27\)

\(=3x^3-36x+27\)

\(\left(x+6\right)^2-2x.\left(x+6\right)+\left(x-6\right).\left(x+6\right)\)

\(=\left(x+6\right).\left(x+6-2x+x-6\right)\)

\(=\left(x+6\right).0\)

\(=0\)

a: \(=x^3-5x^2-x^2+10x+\dfrac{3}{2}x-15=x^3-6x^2+\dfrac{23}{2}x-15\)

b: \(=5x^3-x^4-10x^2+2x^3+5x-x^2-5+x\)

\(=-x^4+7x^3-11x^2+6x-5\)

c: \(=\dfrac{x^3-3x^2+2x^2-6x-x+3}{x-3}=x^2+2x-1\)